Page 125 - Introduction to Statistical Pattern Recognition

3 Hypothesis Testing 107

Fig. 3-20 Relation between po and pLR after transformation.

That is, by the first order approximation, py,,, = p ,,,, . Whether the first order
approximation is good enough or not depends on the distribution.

Example 15: Let us study an exponential distribution and v= 1/4. In
the exponential distribution, p = 0 and E' { x } = Var{ x } . Therefore, the second
order approximation of (3.167) becomes